He studied the relation of Earth tides and earthquakes - finding only the strongest tides noticeably effect the timing of earthquakes,[4] earthquake swarms - finding they are a more general phenomenon than he previously suspected,[5] the inner core - discovering high-frequency seismic waves scattered therein that offer a second line of evidence it is rotating about 0.2 degrees per year,[6][7] the stronger than expected healing of fault zones after an earthquake,[8] and various details of the seismic structure of the mantle.[9] Vidale also contributed an improved method of ray tracing which relied on a finite-difference approximation of the eikonal equation and which has been used widely in both earthquake and reflection seismology.